SQUIDs are a class of very sensitive superconducting measuring devices, whose operation is based on flux quantization and the Josephson effects. After a brief summary of these effects the principles of operation of single and double Josephson junction SQUIDs are dealt with in some detail, including noise processes and estimates of the ultimate sensitivity attainable. Applications of these devices in a wide variety of fields including precise electrical measurement, thermometry, magnetic properties, relativity physics, geophysical measurement and biomagnetism are dealt with.